All the three dimensional Lorentzian metrics admitting three Killing vectors

TL;DR

This paper classifies all three-dimensional Lorentzian metrics with three Killing vectors using a novel formalism that does not depend on isometry group transitivity, revealing a richer spectrum than in Riemannian geometry.

Contribution

The authors provide a complete classification of 3D Lorentzian metrics with three Killing vectors using a new formalism that bypasses traditional transitivity assumptions.

Findings

Rich spectrum of metrics with various Segre types in Lorentzian case

Classification method independent of isometry group transitivity

Identification of all such metrics in three dimensions

Abstract

We obtain all the three-dimensional Lorentzian metrics which admit three Killing vectors. The classification has been done with the aid of the formalism which exploits the obstruction criteria for the Killing equations recently developed by present authors. The current classification method does not rely on the transitivity property of the isometry group. It turns out that the Lorentzian manifold harbors a much richer spectrum of metrics with various Segre types, compared to the Riemannian case.